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2025 Math Kangaroo Grades 7-8 past paper

Suitable for 7-8 Grade, 30 MC questions, coverAlgebra, Geometry, Number Theory.

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30 Questions
75 Minutes
3/4/5 Tiered Scoring
No Calculator
Exam Overview

Exam Overview

2025 years Competitioncreativeincreases, figureshapeand Logic proportionimprove.

DDifficulty

  • 3 pointsQ 1-10
  • 4 pointsQ 11-20
  • 5 pointsQ 21-30

TTopics

  • Algebra25%
  • Geometry20%
  • Number Theory20%
  • Probability15%
  • combination20%

AAwards

Super Gold
Top 1%
90+
Gold
Top 5%
80+
Silver
Top 15%
65+
Bronze
Top 30%
50+
Sample Problems

2025 Kangaroo Level D Sample Problems (8 questions)

Selected problems across difficulty tiers — click an option to check your answer

Q 2Easy 3 pointsAlgebra
solutionequation 3(x-2) = 2(x+1), x = ?
A) 4
B) 6
C) 8

Steps

13 x-6=2 x+2
23 x-2 x=2+6
3x=8
Answer: CExpandbackmovetermcombinedand
Q 5Easy 3 pointsGeometry
right angletriangletwo right anglesiderespectively is 5 and 12, slopeside length how much is?
A) 13
B) 15
C) 17

Steps

1Pythagorean theorem: c2=52+122=25+144=169
2c=13
Answer: A5,12,13 is common Pythagoreannumbergroup
Q 8Easy 3 pointsNumber Theory
100 withinside at the same time is 3 and 7 of multiplehas several?
A) 3
B) 4
C) 5

Steps

1i.e.21 of multiple
221,42,63,84 total 4
Answer: BLCM(3,7)=21
Q 12Medium 4 pointsProbability
1 insidehas 3 redsphere and 5 bluesphere. random take 2 sphere, twoallisredsphereof Probability?
A) 3/28
B) 3/8
C) 9/64

Steps

1totaltakemethod: C(8,2)=28
2tworedtakemethod: C(3,2)=3
3Probability=3/28
Answer: ACombinatorics
Q 16Medium 4 pointsAlgebra
if a+b=7, ab=12, find a2+b2 ofvalue.
A) 25
B) 37
C) 49

Steps

1a2+b2=(a+b)2-2 ab
2=49-24=25
Answer: Abenefitusingcompletelysquareformulaschangeshape
Q 22Hard 5 pointsGeometry
positive hexagonof insideangleand how much is°?
A) 540°
B) 600°
C) 720°

Steps

1nsideshapeinsideangleand=(n-2)×180°
2hexagon=(6-2)×180°=720°
Answer: Cpolygoninsideangleand formulas
Q 26Hard 5 pointscombination
from 1-8 middlechoose 3 differentnumber, makeandis odd. how many kindschoosemethod?
A) 20
B) 28
C) 36

Steps

1andis odd of item: 3 wholeodd or 1 odd 2 even
2odd 4, even 4
33 wholeodd: C(4,3)=4
41 odd 2 even: C(4,1)×C(4,2)=4×6=24
5total 4+24=28 kinds
Answer: Cpointscasesdiscusstheory
Q 30Hard 5 pointsNumber Theory
N is 1 completelysquarenumber, N+99 alsoiscompletelysquarenumber. N maximum how much is?
A) 1
B) 25
C) 2500

Steps

1let N=a2, N+99=b2
2b2-a2=99
3(b-a)(b+a)=99
499=1×99=3×33=9×11
5b-a=1,b+a=99 → a=49,b=50 → N=2401
6b-a=3,b+a=33 → a=15,b=18 → N=225
7b-a=9,b+a=11 → a=1,b=10 → N=1
8maximumN=2401
Answer: Cbecauseexpressionpointssolutionsquaredifference

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